Problem: Solve for $x$ and $y$ using elimination. ${x+4y = 35}$ ${-x-5y = -43}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-y = -8$ $\dfrac{-y}{{-1}} = \dfrac{-8}{{-1}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x+4y = 35}\thinspace$ to find $x$ ${x + 4}{(8)}{= 35}$ $x+32 = 35$ $x+32{-32} = 35{-32}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {-x-5y = -43}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(8)}{= -43}$ ${x = 3}$